Iranian President Hassan Rouhani called the United States a "great" nation Friday in a sharp reversal from his predecessors and expressed hope that at the very least the two governments can stop the escalation of tensions.

Wrapping up his first trip to the United States as Iran's new leader, Rouhani said President Barack Obama struck a new tone in his U.N. speech this week, which he welcomed.

He said he believes the first step to a meeting between the two leaders was taken Thursday at a meeting on Iran's nuclear program, where the foreign ministers of both nations talked for the first time in six years.

"I want it to be the case that this trip will be a first step, and a beginning for better and constructive relations with countries of the world as well as a first step for a better relationship between the two great nations of Iran and the United States of America," Rouhani told a press conference at a hotel near U.N. headquarters.

He expressed hope that "the views of our people, the understanding of each other, will grow, and at the level of the two governments that at the very least we can as a first step stop further escalation of tensions and then reduce tension as a next step and then pave the way for achieving of mutual interests."

Rouhani was upbeat about his four-day visit to New York to attend the U.N. General Assembly's ministerial session, reeling off a long list of leaders he met and saying "I believe that our success was greater than our expectation, especially with the European countries ... and I think that the path really has been paved to expand relations in various centres, key world economies."

Iran's economy has been hit hard by four rounds of U.N. sanctions for its failure to suspend uranium enrichment, a process that can be used to make fuel for both nuclear weapons and nuclear energy. The U.S. and its allies have taken even more devastating measures targeting Iran's ability to conduct international bank transfers and to export oil.

Rouhani said he has a mandate from the Iranian people, who opposed "extremism" and voted for "moderation." He said this has created a "new environment" that could pave the way for better relations with the West.

He said Iran would put forth a proposal at talks in Geneva on Oct. 15-16 aimed at resolving the standoff over his country's nuclear program and easing international sanctions, and he expressed hope that "within a very short time" the nuclear issue will be resolved and relations with the West will improve.

Rouhani said he was encouraged by what he has heard recently from Western officials.

"In speaking with senior European officials and also hearing Mr. Obama ... it seemed that they sounded different compared to the past, and I view that as a positive step to the resettlement of the differences between the Islamic Republic between the Republic of Iran and the West," he said.

He said he did not meet with Obama on the sidelines of the U.N. General Assembly this week because "both sides were convinced that the timetable was too short to plan a meeting of two presidents" and "ensure that its conclusion would be solid."

"What matter to us is the results of such a meeting," Rouhani said.

Iran watchers say Rouhani may have limited time -- possibly a year or less -- to reach a settlement on the nuclear issue before Iran's Supreme Leader Ayatollah Ali Khamenei decides negotiations are fruitless.

In an apparent reference to resistance among hard-liners back home, Rouhani noted that "after 35 years of great tensions between Iran and the United States and a very number of issues that persist ... a meeting of the presidents for the first time will naturally come with complications of its own."

But he said Iran emerged hopeful from a lower-level meeting with the U.S. and its international partners aimed at restarting talks to settle their nuclear standoff.

"We hope that these talks will yield in a short period of time tangible results," Rouhani said.

The upbeat, if guarded, tone by both sides after Thursday's meeting of Iran, the five permanent members of the U.N. Security Council and Germany was seen as a significant step forward after months of stalled talks. It was capped by an unexpected one-on-one meeting between U.S. Secretary of State John Kerry and Iranian Foreign Minister Mohammad Javad Zarif, who shook hands and at one point sat side-by-side in the group talks.

In Vienna, meanwhile, Iranian and U.N. officials held a "constructive" meeting on resuming a probe of allegations that Tehran has worked on atomic arms, officials said Friday, in talks seen as a test of pledges by Rouhani to reduce nuclear tensions.

The upbeat assessment and an agreement to meet again Oct. 28 was a departure from the deadlock left by previous meetings over nearly two years.

At issue are suspicions outlined in reports from the U.N.'s International Atomic Energy Agency that Iran worked secretly on trying to develop nuclear weapons -- something Tehran denies. As part of its probe, the agency is trying to gain access to a sector at Parchin, a sprawling military establishment southeast of Tehran.

Iran says it isn't interested in atomic arms, but the agency suspects the site may have been used to test conventional explosive triggers meant to set off a nuclear blast.

At the United Nations, Kerry said Thursday that he was struck by the "very different tone" from Iran. But along with his European colleagues, he stressed that a single meeting was not enough to assuage international concerns that Iran is seeking to develop nuclear weapons under cover of a civilian atomic energy program.

"Needless to say, one meeting and a change in tone, that was welcome, does not answer those questions," Kerry told reporters. "All of us were pleased that the foreign minister came today and that he did put some possibilities on the table."

Rouhani has come across as a more moderate face of the hard-line clerical regime in Tehran and his pronouncements at the U.N. have raised guarded hopes that progress might be possible. But they have also served as a reminder that the path to that progress will not be quick or easy.

He has steadfastly maintained that any nuclear agreement must recognize Iran's right under international treaties to continue enriching uranium.

AP writers Lara Jakes and Matthew Lee at the United Nations and George Jahn in Vienna contributed to this report.